2010 Fiscal Year Final Research Report
Gauge theory and spin 4-manifolds
| Project/Area Number |
20540089
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| Research Category |
Grant-in-Aid for Scientific Research (C)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Geometry
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| Research Institution | Keio University |
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Principal Investigator |
KAMETANI Yukio Keio University, 理工学部, 准教授 (70253581)
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| Co-Investigator(Kenkyū-buntansha) |
KIYONO Kazuhiko 東京大学, 数理科学研究科, 助教 (40234398)
YOSHIDA Takahiko 明治大学, 研究・知財戦略機構, 研究員 (70451903)
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| Project Period (FY) |
2008 – 2010
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| Keywords | 指数定理 / 局所化 / 共役類 |
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| Research Abstract |
It is well known that topological invariants play important role in geometry. In this research we studied the index of Dirac operators and fundamental groups in different situations. In the former we found a localization of Dirac operators in symplectic action of tori. In the latter we found a geometric interpretation of conjugacy classes of SL(3, Z), which is related to topology of complex surfaces, though it is not completely understood.
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